The 3D Smith Chart


The 3D Smith chart is the first visual design & display tool for active and passive microwave circuits. The tool generalizes the 2D Smith chart on the extended reflection coeffiicent’s plane on the surface of a sphere. The north hemisphere deals with passive circuits while the South with active. Eas- Inductive, West -capacitive

The initial concept was descibed in IEEE microwave and Wirless Letters in the articles ” A 3D Smith chart based on the Riemann Sphere for active and Passive Microwave Circuits” back in 2011 and ” The 3D Smith chart and its Practical Applications- Microwave Journal 2012

The tool ( was in the meantime extended based on the articles publised in Electronics Letters ( on Transducer power gain circles-2014) with two other articles being in Press in Microwave Journal and another one.

The new concepts bring to light the unprecedented capabilities of the 3D Smith chart and a new one ( hyperbolic) to deal with group dealy, qulaity factors and open the possibility for an entire new world of displaying with further applications in  all microwave fields of twhile exploiting the topology of the surfaces in a different way.



andrei1Andrei Muller ( PhD) led the development of the first 3D Smith chart tool. He is currently completing an European Post-Doc grant in Valencia Spain ( February 2017). Andrei also introduced in microwave filter design and synthesis the concepts of ” reflections” and hyperbolic ” reflections” to complement the rotation matrices used  in the lossless and lossy synthesis procedures ” Coupling matrix Filter Synthesis based on Hyperbolic Reflections” IMS San Francisco 2016 and showed the existence of two unseen properties of Foster and Non Foster circuits, Electronics Letters 2015 ” Properties of purely reactive Foster and Non Foster circuits”. Andrei is since may 2016 an Associate Editor of the IEEE Access Journal.



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